Critique: The Illusion of Open-Loop Control

Critique and response context for The Illusion of Open-Loop Control in AffineDrift’s control-affine golf-swing framework.

Critique: The Illusion of Open-Loop Control

The Argument

The AffineDrift framework treats the control input \(u(t)\) (torque) as an exogenous signal—a variable that can be manipulated independently of the state \(x(t)\). The counterfactuals ask “What if \(u(t) = 0\)?”

The Flaw

Human motor control is fundamentally closed-loop. The torque generated by a golfer is a function of the state (feedback) and the motor plan (feedforward). \[ u(t) = u_{FF}(t) + u_{FB}(x(t)) \]

Reflex loops (monosynaptic stretch reflexes, etc.) mean that “passive” motion (\(x\) changing due to drift) automatically generates “active” torque (\(u\) changing due to feedback).

If the clubhead pulls the hands away (drift), the muscles stretch, and the stretch reflex generates a restoring torque (input). This happens within tens of milliseconds.

Therefore, the “Input” \(u\) is not causally independent of the “Drift” \(f(x)\). The drift causes input. By separating them into additive terms \(\dot{x} = f(x) + g(x)u\), the theory obscures this causality. It treats the golfer as an open-loop controller executing a pre-planned tape, ignoring the continuous interplay between mechanics and sensory feedback.

The “Zero Torque” Impossibility

The ZTCF imagines a state where \(u=0\). In a biological system, this is equivalent to:

  1. Total muscle flaccidity.
  2. Complete suppression of stretch reflexes.
  3. Severing of the spinal cord (conceptually).

A conscious golfer cannot “choose” to output zero torque in the face of violent perturbations (like the centrifugal pull of a club). The nervous system defends joint integrity reflexively. Thus, the ZTCF trajectory describes a motion that is not only “passive” but physiologically prohibited.

Recommendations

  1. Distinguish Mechanics from Control: The authors must clarify that the decomposition is strictly mechanical. It calculates the net torque required to sustain the motion, regardless of whether that torque arose from voluntary will or spinal reflex.
  2. Avoid “Golfer’s Intent”: The text should avoid implying that \(\tau_{input}\) represents the golfer’s “effort” or “choice.” It represents the net neuromuscular output, much of which may be reflexive and subconscious.
  3. Future Control Models: A more advanced model would decompose \(u\) into feedforward and feedback components, allowing for a “Zero Voluntary Effort” counterfactual that retains reflexive stabilization.

References

  • Todorov, E., & Jordan, M. I. (2002). Optimal feedback control as a theory of motor coordination. Nature Neuroscience.
  • Prilutsky, B. I., & Zatsiorsky, V. M. (2002). Optimization-based models of muscle coordination.